Stochastic processes with proportional increments and the last-arrival problem - Université Pierre et Marie Curie Accéder directement au contenu
Article Dans Une Revue Stochastic Processes and their Applications Année : 2012

Stochastic processes with proportional increments and the last-arrival problem

Résumé

The notion of stochastic processes with proportional increments is introduced. This notion is of general interest as indicated by its relationship with several stochastic processes, as counting processes, Levy processes, and others, as well as martingales related with these processes. The focus of this article is on the motivation to introduce processes with proportional increments, as instigated by certain characteristics of stopping problems under weak information. We also study some general properties of such processes. These lead to new insights into the mechanism and characterization of Pascal processes. This again will motivate the introduction of more general f-increment processes as well as the analysis of their link with martingales. As a major application we solve the no-information version of the last-arrival problem which was an open problem. Further applications deal with the impact of proportional increments on modelling investment problems, with a new proof of the 1/e-law of best choice, and with other optimal stopping problems

Dates et versions

hal-00730534 , version 1 (10-09-2012)

Identifiants

Citer

F.T. Bruss, Marc Yor. Stochastic processes with proportional increments and the last-arrival problem. Stochastic Processes and their Applications, 2012, 122 (9), pp.3239-3261. ⟨10.1016/j.spa.2012.05.010⟩. ⟨hal-00730534⟩
132 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More